Because it's real. It's no different than saying "That's not how physics/anatomy/psychology works."
If it's operating under a different sort of reality, how are we supposed to relate to it or comprehend the stakes?
Except that's you. You're the one who apparently has no vested interest in a position and therefore can't understand why someone thinks it is important.
Well, because we don't have a word for it. There has to be something particular or unique that is essential to human existence, otherwise we are just animals, and mass murder is not morally worse than the operations of McDonald's. THAT is what I prefer to reserve the term "soul" for, with the body being just a vehicle or garment. So the thing that you see when you look at someone else in T'A'R is like underwear. They can mess with your clothes, even your underwear, but they can't touch the person beneath.

Not sure what you mean.

Yes. I alluded to this previously. It's like a resonance, how we recognize other people's humanity. It doesn't contradict what I am saying, Berelain and Annoura were touching the clothes, while Perrin was running around in his underwear.
I'm not going to argue this point, because Sanderson. Which means I am not as familiar with the passages in question, and I have zero confidence in its reliability as a commentary on the original author's work, anymore than Mat's note to Elayne in the same books is an accurrate barometer of his literacy as Jordan created him.
Also, Hopper's not a person, he's an animal, which probably don't have immortal souls.

No they don't. The One Power is a natural force, like gravity or thermodynamics. It has no morality attached to it, and anyone can use it. It is NOT the opposite of the True Power, which comes directly from the Dark One, otherwise the Forsaken would lose the ability to channel. Not because the Creator forbids it, because he doesn't intervene, but because as they become more attuned to the Shadow, they get out of synch with its opposite, the Light. The One Power and True Power should have more antithetical interaction if they are really opposed as would be the case if the One Power was the Creator's equivalent. The taint on saidin would not simply sit on top, it would actually be attacking or corrupting the male Power, it would have to be surgically excised, not skimmed off. And the One Power should have a similar effect to the taint of the Shadow and True Power as Shadar Logoth did to the taint - they should be both consuming or destroying each other. Now, I think RJ might have dabbled a bit with the idea of the One Power and Shadow being opposing forces, with the comments in the beginning suggesting that Shadowpawn and Darkfriends were repelled by the presence of a channeler, or that channelers could sense Darkfriends, but that is something we never actually see in action. No one as powerful as Rand or as experienced as Cadsuane can detect a Darkfriend, even one in close contact. Mesaana should have had every sister in the Tower in a panic the moment she set foot in the place and Rand or Cadsuane should have had alarm bells going off the moment Semirhage stepped out to meet them. Liandrin and her party should have known Moghedian right off the bat. Those are clearly ideas RJ dropped fairly early in the series, and if channelers give Shadowspawn pause, it is only because of the greater potential threat they represent.
In the first place, it's not invincibility, it's something outside the realm the Power can affect. And if the Creator and the Dark One can be destroyed by the Power (if Rand could have eliminated the Dark One, I'd put it to more to do with his influence on the Pattern at that moment and his interactions with the Dark One allowing him that measure of influence; see above, re:Sanderson), it's because they do interact with the world and have become a part of it. Human souls do not, except via the medium of a human body and the metaphysical "underwear" thereof. Maybe there is something above and behind the Dark One that would have continued on its own, other, plane of existence if Rand had killed the part that affected his world.

I don't know what you mean here.
I sort of think of it that way, not that people are a part of either one, but rather that their actions, thoughts and choices in life have a cumulative effect of attuning the frequency on which their soul exists, to either the Light or Shadow. Or God or whatever the afterlife is in whichever universe they live. It's not that God sits on a throne and says "Not you. You go directly to Hell," it's that one's acts and choices have made one utterly incompatible with God and do not fit in the affiliated afterlife.

That same sort of thing is what gives the Dark One strength in the world of WoT. As the threads of people's lives in the Pattern turn evil they are more like the Shadow and the Pattern becomes more conducive to the Shadow and so the Dark One has more influence, and can accelerate their inclinations to act in accordance with the Shadow. That's why once he could touch the Pattern directly, there was a catastrophic collapse in the fabric of society and standards of human behavior. It's what Siuan refers to when she mentions the rise of evil and tolerance of the same, back in tGH. "What men called evil ten years ago is caprice compared to what is done every day in the streets." It's also why the behavior changes in cities ruled by a Forsaken. The Forsaken, thanks to their connections to the Dark One, are sort of vectors for the Shadow's influence.

Meanwhile, positive influences come only from Rand, rather than all channelers. If the One Power was the stuff of good or the Light, then channelers almost as powerful should be having a lesser effect. Elayne & Aviendha & Min should have been having a secondary effect because of the bond. Instead, those lesser effects come from Mat & Perrin, who are also ta'veren. Rand's special Dragon qualities came not from the Light, or the Creator, but from the Pattern resisting the Dark One's influence and effects. And Rand was able to activate that aspect of his nature by getting his head straight, by putting himself in tune with the Pattern and the way the world was supposed to be, not by giving himself to the Light or kneeling to the Creator. The Creator made the world and the Pattern, setting it up so people could exist and do whatever they were supposed to. There was a plan with built-in self-correcting mechanisms to resist the Dark One's inevitable attempts to mess with it. For the Creator to not interfere, souls could not be part of him, and for the Dark One to be wrong, the same applies. If the Pattern is equally his right and his power and stature are equal or comparable to the Creator, his dominance over the world and people are right and just, in the absence of the Creator upholding his own position. Perrin is right in tDR, he and Moiraine are merely making semantic errors in failing to distinguish between harm or misfortune and actual evil. He is wrong in saying that random accidents hurting people are evil, and Moiraine compounds it by appearing to conflate that stuff with deliberate choices to do wrong and harm others. Perrin's conception of the Pattern as some sort of masterwork of good isn't wrong, it's just that he mistaking the finished plan for the reality. Because that's Perrin. He's spiritually lazy, he wants to believe that there is a plan for the best and all he has to do is follow and obey and everything will work out. He doesn't yet want to see that he has to do his part to make the plan happen, to complete the masterwork of the Pattern. He is right about bad choices and evil deeds going against the Pattern and the Creator's design, but he's wrong in equating those things to a drought or a house fire, just as finding a trove of gold coins is not "good" or of the Light. Good or evil is how you react to the drought or fire or windfall of treasure. Do you compensate your losses at others' expense or hoard what you have rather than share with your fellow sufferers? Do you use the money to help people or to indulge your appetites? These are the sorts of choices that shape your soul and cumulatively make the Pattern a good picture or an image of the Shadow. The Shadow or Dark One or the One Power can inflict the harmful circumstances, but it cannot change your choices and your handling of such circumstances.

That's why I won't believe that anything of the world or Pattern or capable of affecting either can kill or harm a soul, because it is the same thing as taking away those choices. Compulsion can change your perceptions and actions, but it can't change your mind, and that's why it's evil, because it is alienating the physical and metaphysical manifestations of existence, from their essence, which could be called the soul or the will.

The simplist analogy I can think of, is there is hardware and software and a user. One's physical body and the One Power are different forms of hardware, which the soul is the user. The inbetween stuff that the Dark One and Mashadar and channelers can mess with, which connects to T'A'R or through a warder bond is the software.